Week6_2

# Week6_2 - ENGR210 Fall 2011 Examples of 2D systems Roller...

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ENGR210, Fall 2011 1 Examples of 2D systems Roller support The roller support prevents the body from vertical translation . F is an unknown support reaction force. The angle between F and the beam (longitudinal direction) is 90 degrees.

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ENGR210, Fall 2011 2 Pin support The pin support prevents translation of the body in any direction (Therefore, F and Φ are the unknowns to be solved.) Alternatively, support reactions for a pin can be given as F x and F y (because Fcos Φ = Fx, and Fsin Φ = Fy), which is typically easier to deal with. OR
ENGR210, Fall 2011 3 Fixed support A fixed support prevents both translation and rotation of the body , which requires two support forces and one couple moment. Therefore, these unknowns have to be included in a FBD for a system with a fixed support.

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ENGR210, Fall 2011 4 The direction of a reaction force or moment is arbitrary. You can draw an “arrow” in either direction. However, for example, for a roller support, the support cannot “pull” but only “push.” Therefore, some common sense can be used. (After you define the direction of unknown variables (including support reactions) in your FBD, you will develop equilibrium equations to solve for those unknowns. During the processes, the signs of the unknowns has to be consistent with those in the FBD.)
ENGR210, Fall 2011 5 Table 5.1 shows 2D support reactions and the number of unknowns. Memorize them ! Examples (One unknown F (magnitude). The link is also called “short link ” or “two force member ”) (One unknown F (magnitude))

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6 (One unknown F (magnitude)) (Two unknowns F (2 magnitude, or 1 magnitude and 1 direction))
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Week6_2 - ENGR210 Fall 2011 Examples of 2D systems Roller...

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